Originally Posted by Wizofoz
[PBL: Capt Pit Bull has already pointed out that the appropriate way to think of things is as forces causing accelerations, and not motions causing ... forces.]
And I think he's wrong.
An EQUATION means the two sides are EQUAL, meaning they are the same thing. One side doesn't CAUSE the other, both sides ARE each other.
You are correct that equations do not express causality. Indeed, they cannot express causality, because equations, as you point out, are symmetric, whereas causality is not. But just because equations are used, it doesn't mean that you can infer that there is no causality! Indeed, that would go against 350 years of experience with this particular piece of science (which is still valid at low relative velocities).
For example, suppose I drop a ball and it hits the floor. This entire interaction is well described by Newtonian mechanical principles, all expressed in equations as you note. But the action of gravity along with my releasing the ball are causes of its impact with the ground. Similarly, its impact with the ground is not a cause either of gravity or of my dropping it.
Back to the original problem. Say I weigh 80 kgs on the scale. You think I will weigh less (that is, the scale will read less) if the earth spins faster. So you probably think I will weigh more if the earth spins slower. How much would you think I would weigh if the earth just stops rotating? What would be the cause of my weighing that much? Indeed, what would be the cause of my weighing anything at all in any of these scenarios?
PBL